Absolute-length determination of a long-baseline Fabry-Perot cavity by means of resonating modulation sidebands

High precision optical cavity length and width measurements using double modulation

We use doubly phase modulated light to measure both the length and the linewidth of an optical resonator with high precision. The first modulation is at RF frequencies and is set near a multiple of the free spectral range, whereas the second modulation is at audio frequencies to eliminate offset errors at DC. The light in transmission or in reflection of the optical resonator is demodulated while sweeping the RF frequency over the optical resonance. We derive expressions for the demodulated power in transmission, and show that the zero crossings of the demodulated signal in transmission serve as a precise measure of the cavity linewidth at half maximum intensity. We demonstrate the technique on two resonant cavities, with lengths 16 m and a 4 km, and achieve an absolute length accuracy as low as 70 ppb. The cavity width for the 16 m cavity was determined with an accuracy of approximately 6000 ppm. Through an analysis of the systematic errors we show that this result could be substantially improved with the reduction of technical sources of uncertainty.

Technique for in situ measurement of free spectral range and transverse mode spacing of optical cavities

Length and g-factor are fundamental parameters that characterize optical cavities. We developed a technique to measure these parameters in situ by determining the frequency spacing between the resonances of fundamental and spatial modes of an optical cavity. Two laser beams are injected into the cavity, and their relative frequency is scanned by a phase-lock loop, while the cavity is locked to either laser. The measurement of the amplitude of their beat note in transmission reveals the resonances of the longitudinal and the transverse modes of the cavity and their spacing. This method proves particularly useful to characterize complex optical systems, including very long and/or coupled optical cavities, as in gravitational-wave interferometers. This technique and the results of its application to the coupled cavities of a 40 m-long gravitational-wave interferometer prototype are presented here.

Compact vibration isolation and suspension for Australian International Gravitational Observatory: performance in a 72 m Fabry Perot cavity

This paper describes the first demonstration of vibration isolation and suspension systems, which have been developed with view to application in the proposed Australian International Gravitational Observatory. In order to achieve optimal performance at low frequencies new components and techniques have been combined to create a compact advanced vibration isolator structure. The design includes two stages of horizontal preisolation and one stage of vertical preisolation with resonant frequencies approximately 100 mHz. The nested structure facilitates a compact design and enables horizontal preisolation stages to be configured to create a superspring configuration, where active feedback can enable performance close to the limit set by seismic tilt coupling. The preisolation stages are combined with multistage three-dimensional (3D) pendulums. Two isolators suspending mirror test masses have been developed to form a 72 m optical cavity with finesse approximately 700 in order to test their performance. The suitability of the isolators for use in suspended optical cavities is demonstrated through their ease of locking, long term stability, and low residual motion. An accompanying paper presents the local control system and shows how simple upgrades can substantially improve residual motion performance.

Nanometer measurement with a dual fabry-perot interferometer

On the basis of analyzing sinusoidal phase-modulating Fabry-Perot interferometry, a method, believed to be novel, is proposed for achieving nanometer measurement accuracy by measuring the time interval between equal amplitudes of the two elementary frequency signals of the transmitted intensities of a dual Fabry-Perot interferometer. A nanometer measurement system based on the method was designed and tested. The experimental results show that the displacement resolution of the system is 0.32 nm at a 1-kHz modulating signal.